xref: /petsc/src/ksp/pc/impls/bjacobi/bjkokkos/bjkokkos.kokkos.cxx (revision ed00a6c129cbc4f1b4754b50ab0c4e7536acfadd)
1 #include <petscvec_kokkos.hpp>
2 #include <petsc/private/deviceimpl.h>
3 #include <petsc/private/pcimpl.h>
4 #include <petsc/private/kspimpl.h>
5 #include <petscksp.h> /*I "petscksp.h" I*/
6 #include <../src/mat/impls/aij/mpi/mpiaij.h>
7 #include <../src/mat/impls/aij/mpi/kokkos/mpiaijkok.hpp>
8 #include "petscsection.h"
9 #include <petscdmcomposite.h>
10 #include "Kokkos_Core.hpp"
11 
12 #include <../src/mat/impls/aij/seq/aij.h>
13 #include <../src/mat/impls/aij/seq/kokkos/aijkok.hpp>
14 
15 #if defined(PETSC_HAVE_CUDA)
16   #include <nvToolsExt.h>
17 #endif
18 
19 #include <petscdevice_cupm.h>
20 
21 #define PCBJKOKKOS_SHARED_LEVEL 1 // 0 is shared, 1 is global
22 #define PCBJKOKKOS_VEC_SIZE     16
23 #define PCBJKOKKOS_TEAM_SIZE    16
24 
25 #define PCBJKOKKOS_VERBOSE_LEVEL 1
26 
27 typedef Kokkos::DefaultExecutionSpace exec_space;
28 using layout           = Kokkos::LayoutRight;
29 using IntView          = Kokkos::View<PetscInt **, layout, exec_space>;
30 using AMatrixValueView = const Kokkos::View<PetscScalar **, layout, exec_space>;
31 using XYType           = const Kokkos::View<PetscScalar **, layout, exec_space>;
32 
33 typedef enum {
34   BATCH_KSP_BICG_IDX,
35   BATCH_KSP_TFQMR_IDX,
36   BATCH_KSP_GMRES_IDX,
37   NUM_BATCH_TYPES
38 } KSPIndex;
39 typedef struct {
40   Vec                                               vec_diag;
41   PetscInt                                          nBlocks; /* total number of blocks */
42   PetscInt                                          n;       // cache host version of d_bid_eqOffset_k[nBlocks]
43   KSP                                               ksp;     // Used just for options. Should have one for each block
44   Kokkos::View<PetscInt *, Kokkos::LayoutRight>    *d_bid_eqOffset_k;
45   Kokkos::View<PetscScalar *, Kokkos::LayoutRight> *d_idiag_k;
46   Kokkos::View<PetscInt *>                         *d_isrow_k;
47   Kokkos::View<PetscInt *>                         *d_isicol_k;
48   KSPIndex                                          ksp_type_idx;
49   PetscInt                                          nwork;
50   PetscInt                                          const_block_size; // used to decide to use shared memory for work vectors
51   PetscInt                                         *dm_Nf;            // Number of fields in each DM
52   PetscInt                                          num_dms;
53   // diagnostics
54   PetscBool reason;
55   PetscBool monitor;
56   PetscInt  batch_target;
57   PetscInt  nsolves_team;
58   PetscInt  max_nits;
59   // caches
60   IntView          *rowOffsets;
61   IntView          *colIndices;
62   XYType           *batch_b;
63   XYType           *batch_x;
64   AMatrixValueView *batch_values;
65 } PC_PCBJKOKKOS;
66 
67 #if defined(PETSC_HAVE_KOKKOS_KERNELS_GMRES)
68   #include <fstream>
69 
70   #include "Kokkos_Timer.hpp"
71   #include "Kokkos_Random.hpp"
72   #include "Kokkos_UnorderedMap.hpp"
73   #include "Kokkos_Sort.hpp"
74 
75   /// KokkosKernels headers
76   #include "KokkosBatched_Util.hpp"
77   #include "KokkosBatched_Vector.hpp"
78 
79   #include <Kokkos_ArithTraits.hpp>
80   #include <KokkosBatched_Util.hpp>
81   #include <KokkosBatched_Vector.hpp>
82   #include <KokkosBatched_Copy_Decl.hpp>
83   #include <KokkosBatched_Copy_Impl.hpp>
84   #include <KokkosBatched_AddRadial_Decl.hpp>
85   #include <KokkosBatched_AddRadial_Impl.hpp>
86   #include <KokkosBatched_Gemm_Decl.hpp>
87   #include <KokkosBatched_Gemm_Serial_Impl.hpp>
88   #include <KokkosBatched_Gemm_Team_Impl.hpp>
89   #include <KokkosBatched_Gemv_Decl.hpp>
90   #include <KokkosBatched_Gemv_Serial_Impl.hpp>
91   #include <KokkosBatched_Gemv_Team_Impl.hpp>
92   #include <KokkosBatched_Trsm_Decl.hpp>
93   #include <KokkosBatched_Trsm_Serial_Impl.hpp>
94   #include <KokkosBatched_Trsm_Team_Impl.hpp>
95   #include <KokkosBatched_Trsv_Decl.hpp>
96   #include <KokkosBatched_Trsv_Serial_Impl.hpp>
97   #include <KokkosBatched_Trsv_Team_Impl.hpp>
98   #include <KokkosBatched_LU_Decl.hpp>
99   #include <KokkosBatched_LU_Serial_Impl.hpp>
100   #include <KokkosBatched_LU_Team_Impl.hpp>
101   #include <KokkosSparse_CrsMatrix.hpp>
102   #include "KokkosBatched_Spmv.hpp"
103   #include "KokkosBatched_CrsMatrix.hpp"
104   #include "KokkosBatched_Krylov_Handle.hpp"
105   #include "KokkosBatched_GMRES.hpp"
106   #include "KokkosBatched_JacobiPrec.hpp"
107 
108 template <typename DeviceType, typename ValuesViewType, typename IntView, typename VectorViewType, typename KrylovHandleType>
109 struct Functor_TestBatchedTeamVectorGMRES {
110   const ValuesViewType _D;
111   const ValuesViewType _diag;
112   const IntView        _r;
113   const IntView        _c;
114   const VectorViewType _X;
115   const VectorViewType _B;
116   const int            _N_team, _team_size, _vector_length;
117   const int            _N_iteration;
118   const double         _tol;
119   const int            _ortho_strategy;
120   const int            _scratch_pad_level;
121   KrylovHandleType     _handle;
122 
123   KOKKOS_INLINE_FUNCTION
124   Functor_TestBatchedTeamVectorGMRES(const ValuesViewType &D, const IntView &r, const IntView &c, const VectorViewType &X, const VectorViewType &B, const int N_team, const int team_size, const int vector_length, const int N_iteration, const double tol, const int ortho_strategy, const int scratch_pad_level, KrylovHandleType &handle) :
125     _D(D), _r(r), _c(c), _X(X), _B(B), _N_team(N_team), _team_size(team_size), _vector_length(vector_length), _N_iteration(N_iteration), _tol(tol), _ortho_strategy(ortho_strategy), _scratch_pad_level(scratch_pad_level), _handle(handle)
126   {
127   }
128 
129   KOKKOS_INLINE_FUNCTION
130   Functor_TestBatchedTeamVectorGMRES(const ValuesViewType &D, const ValuesViewType &diag, const IntView &r, const IntView &c, const VectorViewType &X, const VectorViewType &B, const int N_team, const int team_size, const int vector_length, const int N_iteration, const double tol, int ortho_strategy, const int scratch_pad_level, KrylovHandleType &handle) :
131     _D(D), _diag(diag), _r(r), _c(c), _X(X), _B(B), _N_team(N_team), _team_size(team_size), _vector_length(vector_length), _N_iteration(N_iteration), _tol(tol), _ortho_strategy(ortho_strategy), _scratch_pad_level(scratch_pad_level), _handle(handle)
132   {
133   }
134 
135   template <typename MemberType>
136   KOKKOS_INLINE_FUNCTION void operator()(const MemberType &member) const
137   {
138     const int first_matrix = static_cast<int>(member.league_rank()) * _N_team;
139     const int N            = _D.extent(0);
140     const int last_matrix  = (static_cast<int>(member.league_rank() + 1) * _N_team < N ? static_cast<int>(member.league_rank() + 1) * _N_team : N);
141     const int graphID      = static_cast<int>(member.league_rank());
142     using TeamVectorCopy1D = KokkosBatched::TeamVectorCopy<MemberType, KokkosBatched::Trans::NoTranspose, 1>;
143 
144     auto d                         = Kokkos::subview(_D, Kokkos::make_pair(first_matrix, last_matrix), Kokkos::ALL);
145     auto x                         = Kokkos::subview(_X, Kokkos::make_pair(first_matrix, last_matrix), Kokkos::ALL);
146     auto b                         = Kokkos::subview(_B, Kokkos::make_pair(first_matrix, last_matrix), Kokkos::ALL);
147     using ScratchPadIntViewType    = Kokkos::View<typename IntView::non_const_value_type *, typename IntView::array_layout, typename IntView::execution_space::scratch_memory_space>;
148     using ScratchPadValuesViewType = Kokkos::View<typename ValuesViewType::non_const_value_type **, typename ValuesViewType::array_layout, typename ValuesViewType::execution_space::scratch_memory_space>;
149 
150     using Operator = KokkosBatched::CrsMatrix<ValuesViewType, ScratchPadIntViewType>;
151     ScratchPadIntViewType r(member.team_scratch(1), _r.extent(1));
152     ScratchPadIntViewType c(member.team_scratch(1), _c.extent(1));
153 
154     TeamVectorCopy1D::invoke(member, Kokkos::subview(_r, graphID, Kokkos::ALL), r);
155     TeamVectorCopy1D::invoke(member, Kokkos::subview(_c, graphID, Kokkos::ALL), c);
156     Operator A(d, r, c);
157 
158     ScratchPadValuesViewType diag(member.team_scratch(1), last_matrix - first_matrix, _diag.extent(1));
159     using PrecOperator = KokkosBatched::JacobiPrec<ScratchPadValuesViewType>;
160 
161     KokkosBatched::TeamVectorCopy<MemberType>::invoke(member, Kokkos::subview(_diag, Kokkos::make_pair(first_matrix, last_matrix), Kokkos::ALL), diag);
162     PrecOperator P(diag);
163     P.setComputedInverse();
164 
165     KokkosBatched::TeamVectorGMRES<MemberType>::template invoke<Operator, VectorViewType, PrecOperator, KrylovHandleType>(member, A, b, x, P, _handle);
166   }
167   inline double run(PC pc)
168   {
169     typedef typename ValuesViewType::value_type value_type;
170     std::string                                 name("KokkosBatched::Test::TeamVectorGMRES");
171     Kokkos::Timer                               timer;
172     Kokkos::Profiling::pushRegion(name.c_str());
173 
174     Kokkos::TeamPolicy<DeviceType> auto_policy(ceil(1. * _D.extent(0) / _N_team), Kokkos::AUTO(), Kokkos::AUTO());
175     Kokkos::TeamPolicy<DeviceType> tuned_policy(ceil(1. * _D.extent(0) / _N_team), _team_size, _vector_length);
176     Kokkos::TeamPolicy<DeviceType> policy;
177 
178     if (_team_size < 1) policy = auto_policy;
179     else policy = tuned_policy;
180 
181     _handle.set_max_iteration(_N_iteration);
182     _handle.set_tolerance(_tol);
183     _handle.set_ortho_strategy(_ortho_strategy);
184     _handle.set_scratch_pad_level(_scratch_pad_level);
185     _handle.set_compute_last_residual(true);
186 
187     int maximum_iteration = _handle.get_max_iteration();
188 
189     using ScalarType = typename ValuesViewType::non_const_value_type;
190     using Layout     = typename ValuesViewType::array_layout;
191     using EXSP       = typename ValuesViewType::execution_space;
192 
193     using MagnitudeType = typename Kokkos::Details::ArithTraits<ScalarType>::mag_type;
194 
195     using ViewType1D    = Kokkos::View<MagnitudeType *, Layout, EXSP>;
196     using ViewType2D    = Kokkos::View<ScalarType **, Layout, EXSP>;
197     using ViewType3D    = Kokkos::View<ScalarType ***, Layout, EXSP>;
198     using IntViewType1D = Kokkos::View<PetscInt *, Layout, EXSP>;
199 
200     size_t bytes_1D      = ViewType2D::shmem_size(_N_team, 1);
201     size_t bytes_row_ptr = IntViewType1D::shmem_size(_r.extent(1));
202     size_t bytes_col_idc = IntViewType1D::shmem_size(_c.extent(1));
203     size_t bytes_2D_1    = ViewType2D::shmem_size(_N_team, _X.extent(1));
204     size_t bytes_2D_2    = ViewType2D::shmem_size(_N_team, maximum_iteration + 1);
205 
206     size_t bytes_diag = bytes_2D_1;
207     size_t bytes_tmp  = 2 * bytes_2D_1 + 2 * bytes_1D + bytes_2D_2;
208 
209     policy.set_scratch_size(0, Kokkos::PerTeam(bytes_tmp));
210     policy.set_scratch_size(1, Kokkos::PerTeam(bytes_col_idc + bytes_row_ptr + bytes_diag));
211     PetscCall(PetscInfo(pc, "%d scratch memory(0) = %d + %d + %d bytes_diag=%d; %d scratch memory(1); %d maximum_iterations\n", (int)(bytes_tmp), 2 * (int)bytes_2D_1, 2 * (int)bytes_1D, (int)bytes_2D_2, (int)bytes_diag, (int)(bytes_row_ptr + bytes_col_idc + bytes_diag), (int)maximum_iteration));
212     exec_space().fence();
213     timer.reset();
214     Kokkos::parallel_for(name.c_str(), policy, *this);
215     exec_space().fence();
216     double sec = timer.seconds();
217 
218     return sec;
219   }
220 };
221 #endif // KK GMRES
222 
223 typedef Kokkos::TeamPolicy<>::member_type team_member;
224 
225 static PetscErrorCode PCBJKOKKOSCreateKSP_BJKOKKOS(PC pc)
226 {
227   const char    *prefix;
228   PC_PCBJKOKKOS *jac = (PC_PCBJKOKKOS *)pc->data;
229   DM             dm;
230 
231   PetscFunctionBegin;
232   PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &jac->ksp));
233   PetscCall(KSPSetErrorIfNotConverged(jac->ksp, pc->erroriffailure));
234   PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->ksp, (PetscObject)pc, 1));
235   PetscCall(PCGetOptionsPrefix(pc, &prefix));
236   PetscCall(KSPSetOptionsPrefix(jac->ksp, prefix));
237   PetscCall(KSPAppendOptionsPrefix(jac->ksp, "pc_bjkokkos_"));
238   PetscCall(PCGetDM(pc, &dm));
239   if (dm) {
240     PetscCall(KSPSetDM(jac->ksp, dm));
241     PetscCall(KSPSetDMActive(jac->ksp, PETSC_FALSE));
242   }
243   jac->reason       = PETSC_FALSE;
244   jac->monitor      = PETSC_FALSE;
245   jac->batch_target = -1;
246   jac->nsolves_team = 1;
247   jac->ksp->max_it  = 50; // this is really for GMRES w/o restarts
248   PetscFunctionReturn(PETSC_SUCCESS);
249 }
250 
251 // y <-- Ax
252 KOKKOS_INLINE_FUNCTION PetscErrorCode MatMult(const team_member team, const PetscInt *glb_Aai, const PetscInt *glb_Aaj, const PetscScalar *glb_Aaa, const PetscInt *r, const PetscInt *ic, const PetscInt start, const PetscInt end, const PetscScalar *x_loc, PetscScalar *y_loc)
253 {
254   Kokkos::parallel_for(Kokkos::TeamThreadRange(team, start, end), [=](const int rowb) {
255     int                rowa = ic[rowb];
256     int                n    = glb_Aai[rowa + 1] - glb_Aai[rowa];
257     const PetscInt    *aj   = glb_Aaj + glb_Aai[rowa]; // global
258     const PetscScalar *aa   = glb_Aaa + glb_Aai[rowa];
259     PetscScalar        sum;
260     Kokkos::parallel_reduce(
261       Kokkos::ThreadVectorRange(team, n), [=](const int i, PetscScalar &lsum) { lsum += aa[i] * x_loc[r[aj[i]] - start]; }, sum);
262     Kokkos::single(Kokkos::PerThread(team), [=]() { y_loc[rowb - start] = sum; });
263   });
264   team.team_barrier();
265   return PETSC_SUCCESS;
266 }
267 
268 // temp buffer per thread with reduction at end?
269 KOKKOS_INLINE_FUNCTION PetscErrorCode MatMultTranspose(const team_member team, const PetscInt *glb_Aai, const PetscInt *glb_Aaj, const PetscScalar *glb_Aaa, const PetscInt *r, const PetscInt *ic, const PetscInt start, const PetscInt end, const PetscScalar *x_loc, PetscScalar *y_loc)
270 {
271   Kokkos::parallel_for(Kokkos::TeamVectorRange(team, end - start), [=](int i) { y_loc[i] = 0; });
272   team.team_barrier();
273   Kokkos::parallel_for(Kokkos::TeamThreadRange(team, start, end), [=](const int rowb) {
274     int                rowa = ic[rowb];
275     int                n    = glb_Aai[rowa + 1] - glb_Aai[rowa];
276     const PetscInt    *aj   = glb_Aaj + glb_Aai[rowa]; // global
277     const PetscScalar *aa   = glb_Aaa + glb_Aai[rowa];
278     const PetscScalar  xx   = x_loc[rowb - start]; // rowb = ic[rowa] = ic[r[rowb]]
279     Kokkos::parallel_for(Kokkos::ThreadVectorRange(team, n), [=](const int &i) {
280       PetscScalar val = aa[i] * xx;
281       Kokkos::atomic_fetch_add(&y_loc[r[aj[i]] - start], val);
282     });
283   });
284   team.team_barrier();
285   return PETSC_SUCCESS;
286 }
287 
288 typedef struct Batch_MetaData_TAG {
289   PetscInt           flops;
290   PetscInt           its;
291   KSPConvergedReason reason;
292 } Batch_MetaData;
293 
294 // Solve A(BB^-1)x = y with TFQMR. Right preconditioned to get un-preconditioned residual
295 KOKKOS_INLINE_FUNCTION PetscErrorCode BJSolve_TFQMR(const team_member team, const PetscInt *glb_Aai, const PetscInt *glb_Aaj, const PetscScalar *glb_Aaa, const PetscInt *r, const PetscInt *ic, PetscScalar *work_space_global, const int stride_global, const int nShareVec, PetscScalar *work_space_shared, const int stride_shared, PetscReal rtol, PetscReal atol, PetscReal dtol, PetscInt maxit, Batch_MetaData *metad, const PetscInt start, const PetscInt end, const PetscScalar glb_idiag[], const PetscScalar *glb_b, PetscScalar *glb_x, bool monitor)
296 {
297   using Kokkos::parallel_for;
298   using Kokkos::parallel_reduce;
299   int                Nblk = end - start, i, m, stride = stride_shared, idx = 0;
300   PetscReal          dp, dpold, w, dpest, tau, psi, cm, r0;
301   const PetscScalar *Diag = &glb_idiag[start];
302   PetscScalar       *ptr  = work_space_shared, rho, rhoold, a, s, b, eta, etaold, psiold, cf, dpi;
303 
304   if (idx++ == nShareVec) {
305     ptr    = work_space_global;
306     stride = stride_global;
307   }
308   PetscScalar *XX = ptr;
309   ptr += stride;
310   if (idx++ == nShareVec) {
311     ptr    = work_space_global;
312     stride = stride_global;
313   }
314   PetscScalar *R = ptr;
315   ptr += stride;
316   if (idx++ == nShareVec) {
317     ptr    = work_space_global;
318     stride = stride_global;
319   }
320   PetscScalar *RP = ptr;
321   ptr += stride;
322   if (idx++ == nShareVec) {
323     ptr    = work_space_global;
324     stride = stride_global;
325   }
326   PetscScalar *V = ptr;
327   ptr += stride;
328   if (idx++ == nShareVec) {
329     ptr    = work_space_global;
330     stride = stride_global;
331   }
332   PetscScalar *T = ptr;
333   ptr += stride;
334   if (idx++ == nShareVec) {
335     ptr    = work_space_global;
336     stride = stride_global;
337   }
338   PetscScalar *Q = ptr;
339   ptr += stride;
340   if (idx++ == nShareVec) {
341     ptr    = work_space_global;
342     stride = stride_global;
343   }
344   PetscScalar *P = ptr;
345   ptr += stride;
346   if (idx++ == nShareVec) {
347     ptr    = work_space_global;
348     stride = stride_global;
349   }
350   PetscScalar *U = ptr;
351   ptr += stride;
352   if (idx++ == nShareVec) {
353     ptr    = work_space_global;
354     stride = stride_global;
355   }
356   PetscScalar *D = ptr;
357   ptr += stride;
358   if (idx++ == nShareVec) {
359     ptr    = work_space_global;
360     stride = stride_global;
361   }
362   PetscScalar *AUQ = V;
363 
364   // init: get b, zero x
365   parallel_for(Kokkos::TeamVectorRange(team, start, end), [=](int rowb) {
366     int rowa         = ic[rowb];
367     R[rowb - start]  = glb_b[rowa];
368     XX[rowb - start] = 0;
369   });
370   team.team_barrier();
371   parallel_reduce(
372     Kokkos::TeamVectorRange(team, Nblk), [=](const int idx, PetscScalar &lsum) { lsum += R[idx] * PetscConj(R[idx]); }, dpi);
373   team.team_barrier();
374   r0 = dp = PetscSqrtReal(PetscRealPart(dpi));
375 // diagnostics
376 #if defined(PETSC_USE_DEBUG) && !defined(PETSC_HAVE_SYCL)
377   if (monitor) Kokkos::single(Kokkos::PerTeam(team), [=]() { printf("%3d KSP Residual norm %14.12e \n", 0, (double)dp); });
378 #endif
379   if (dp < atol) {
380     metad->reason = KSP_CONVERGED_ATOL_NORMAL;
381     return PETSC_SUCCESS;
382   }
383   if (0 == maxit) {
384     metad->reason = KSP_DIVERGED_ITS;
385     return PETSC_SUCCESS;
386   }
387 
388   /* Make the initial Rp = R */
389   parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) { RP[idx] = R[idx]; });
390   team.team_barrier();
391   /* Set the initial conditions */
392   etaold = 0.0;
393   psiold = 0.0;
394   tau    = dp;
395   dpold  = dp;
396 
397   /* rhoold = (r,rp)     */
398   parallel_reduce(
399     Kokkos::TeamVectorRange(team, Nblk), [=](const int idx, PetscScalar &dot) { dot += R[idx] * PetscConj(RP[idx]); }, rhoold);
400   team.team_barrier();
401   parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) {
402     U[idx] = R[idx];
403     P[idx] = R[idx];
404     T[idx] = Diag[idx] * P[idx];
405     D[idx] = 0;
406   });
407   team.team_barrier();
408   static_cast<void>(MatMult(team, glb_Aai, glb_Aaj, glb_Aaa, r, ic, start, end, T, V));
409 
410   i = 0;
411   do {
412     /* s <- (v,rp)          */
413     parallel_reduce(
414       Kokkos::TeamVectorRange(team, Nblk), [=](const int idx, PetscScalar &dot) { dot += V[idx] * PetscConj(RP[idx]); }, s);
415     team.team_barrier();
416     a = rhoold / s; /* a <- rho / s         */
417     /* q <- u - a v    VecWAXPY(w,alpha,x,y): w = alpha x + y.     */
418     /* t <- u + q           */
419     parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) {
420       Q[idx] = U[idx] - a * V[idx];
421       T[idx] = U[idx] + Q[idx];
422     });
423     team.team_barrier();
424     // KSP_PCApplyBAorAB
425     parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) { T[idx] = Diag[idx] * T[idx]; });
426     team.team_barrier();
427     static_cast<void>(MatMult(team, glb_Aai, glb_Aaj, glb_Aaa, r, ic, start, end, T, AUQ));
428     /* r <- r - a K (u + q) */
429     parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) { R[idx] = R[idx] - a * AUQ[idx]; });
430     team.team_barrier();
431     parallel_reduce(
432       Kokkos::TeamVectorRange(team, Nblk), [=](const int idx, PetscScalar &lsum) { lsum += R[idx] * PetscConj(R[idx]); }, dpi);
433     team.team_barrier();
434     dp = PetscSqrtReal(PetscRealPart(dpi));
435     for (m = 0; m < 2; m++) {
436       if (!m) w = PetscSqrtReal(dp * dpold);
437       else w = dp;
438       psi = w / tau;
439       cm  = 1.0 / PetscSqrtReal(1.0 + psi * psi);
440       tau = tau * psi * cm;
441       eta = cm * cm * a;
442       cf  = psiold * psiold * etaold / a;
443       if (!m) {
444         /* D = U + cf D */
445         parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) { D[idx] = U[idx] + cf * D[idx]; });
446       } else {
447         /* D = Q + cf D */
448         parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) { D[idx] = Q[idx] + cf * D[idx]; });
449       }
450       team.team_barrier();
451       parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) { XX[idx] = XX[idx] + eta * D[idx]; });
452       team.team_barrier();
453       dpest = PetscSqrtReal(2 * i + m + 2.0) * tau;
454 #if defined(PETSC_USE_DEBUG) && !defined(PETSC_HAVE_SYCL)
455       if (monitor && m == 1) Kokkos::single(Kokkos::PerTeam(team), [=]() { printf("%3d KSP Residual norm %14.12e \n", i + 1, (double)dpest); });
456 #endif
457       if (dpest < atol) {
458         metad->reason = KSP_CONVERGED_ATOL_NORMAL;
459         goto done;
460       }
461       if (dpest / r0 < rtol) {
462         metad->reason = KSP_CONVERGED_RTOL_NORMAL;
463         goto done;
464       }
465 #if defined(PETSC_USE_DEBUG) && !defined(PETSC_HAVE_SYCL)
466       if (dpest / r0 > dtol) {
467         metad->reason = KSP_DIVERGED_DTOL;
468         Kokkos::single(Kokkos::PerTeam(team), [=]() { printf("ERROR block %d diverged: %d it, res=%e, r_0=%e\n", team.league_rank(), i, dpest, r0); });
469         goto done;
470       }
471 #else
472       if (dpest / r0 > dtol) {
473         metad->reason = KSP_DIVERGED_DTOL;
474         goto done;
475       }
476 #endif
477       if (i + 1 == maxit) {
478         metad->reason = KSP_DIVERGED_ITS;
479         goto done;
480       }
481 
482       etaold = eta;
483       psiold = psi;
484     }
485 
486     /* rho <- (r,rp)       */
487     parallel_reduce(
488       Kokkos::TeamVectorRange(team, Nblk), [=](const int idx, PetscScalar &dot) { dot += R[idx] * PetscConj(RP[idx]); }, rho);
489     team.team_barrier();
490     b = rho / rhoold; /* b <- rho / rhoold   */
491     /* u <- r + b q        */
492     /* p <- u + b(q + b p) */
493     parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) {
494       U[idx] = R[idx] + b * Q[idx];
495       Q[idx] = Q[idx] + b * P[idx];
496       P[idx] = U[idx] + b * Q[idx];
497     });
498     /* v <- K p  */
499     team.team_barrier();
500     parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) { T[idx] = Diag[idx] * P[idx]; });
501     team.team_barrier();
502     static_cast<void>(MatMult(team, glb_Aai, glb_Aaj, glb_Aaa, r, ic, start, end, T, V));
503 
504     rhoold = rho;
505     dpold  = dp;
506 
507     i++;
508   } while (i < maxit);
509 done:
510   // KSPUnwindPreconditioner
511   parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) { XX[idx] = Diag[idx] * XX[idx]; });
512   team.team_barrier();
513   // put x into Plex order
514   parallel_for(Kokkos::TeamVectorRange(team, start, end), [=](int rowb) {
515     int rowa    = ic[rowb];
516     glb_x[rowa] = XX[rowb - start];
517   });
518   metad->its = i + 1;
519   if (1) {
520     int nnz;
521     parallel_reduce(
522       Kokkos::TeamVectorRange(team, start, end), [=](const int idx, int &lsum) { lsum += (glb_Aai[idx + 1] - glb_Aai[idx]); }, nnz);
523     metad->flops = 2 * (metad->its * (10 * Nblk + 2 * nnz) + 5 * Nblk);
524   } else {
525     metad->flops = 2 * (metad->its * (10 * Nblk + 2 * 50 * Nblk) + 5 * Nblk); // guess
526   }
527   return PETSC_SUCCESS;
528 }
529 
530 // Solve Ax = y with biCG
531 KOKKOS_INLINE_FUNCTION PetscErrorCode BJSolve_BICG(const team_member team, const PetscInt *glb_Aai, const PetscInt *glb_Aaj, const PetscScalar *glb_Aaa, const PetscInt *r, const PetscInt *ic, PetscScalar *work_space_global, const int stride_global, const int nShareVec, PetscScalar *work_space_shared, const int stride_shared, PetscReal rtol, PetscReal atol, PetscReal dtol, PetscInt maxit, Batch_MetaData *metad, const PetscInt start, const PetscInt end, const PetscScalar glb_idiag[], const PetscScalar *glb_b, PetscScalar *glb_x, bool monitor)
532 {
533   using Kokkos::parallel_for;
534   using Kokkos::parallel_reduce;
535   int                Nblk = end - start, i, stride = stride_shared, idx = 0; // start in shared mem
536   PetscReal          dp, r0;
537   const PetscScalar *Di  = &glb_idiag[start];
538   PetscScalar       *ptr = work_space_shared, dpi, a = 1.0, beta, betaold = 1.0, b, b2, ma, mac;
539 
540   if (idx++ == nShareVec) {
541     ptr    = work_space_global;
542     stride = stride_global;
543   }
544   PetscScalar *XX = ptr;
545   ptr += stride;
546   if (idx++ == nShareVec) {
547     ptr    = work_space_global;
548     stride = stride_global;
549   }
550   PetscScalar *Rl = ptr;
551   ptr += stride;
552   if (idx++ == nShareVec) {
553     ptr    = work_space_global;
554     stride = stride_global;
555   }
556   PetscScalar *Zl = ptr;
557   ptr += stride;
558   if (idx++ == nShareVec) {
559     ptr    = work_space_global;
560     stride = stride_global;
561   }
562   PetscScalar *Pl = ptr;
563   ptr += stride;
564   if (idx++ == nShareVec) {
565     ptr    = work_space_global;
566     stride = stride_global;
567   }
568   PetscScalar *Rr = ptr;
569   ptr += stride;
570   if (idx++ == nShareVec) {
571     ptr    = work_space_global;
572     stride = stride_global;
573   }
574   PetscScalar *Zr = ptr;
575   ptr += stride;
576   if (idx++ == nShareVec) {
577     ptr    = work_space_global;
578     stride = stride_global;
579   }
580   PetscScalar *Pr = ptr;
581   ptr += stride;
582 
583   /*     r <- b (x is 0) */
584   parallel_for(Kokkos::TeamVectorRange(team, start, end), [=](int rowb) {
585     int rowa         = ic[rowb];
586     Rl[rowb - start] = Rr[rowb - start] = glb_b[rowa];
587     XX[rowb - start]                    = 0;
588   });
589   team.team_barrier();
590   /*     z <- Br         */
591   parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) {
592     Zr[idx] = Di[idx] * Rr[idx];
593     Zl[idx] = Di[idx] * Rl[idx];
594   });
595   team.team_barrier();
596   /*    dp <- r'*r       */
597   parallel_reduce(
598     Kokkos::TeamVectorRange(team, Nblk), [=](const int idx, PetscScalar &lsum) { lsum += Rr[idx] * PetscConj(Rr[idx]); }, dpi);
599   team.team_barrier();
600   r0 = dp = PetscSqrtReal(PetscRealPart(dpi));
601 #if defined(PETSC_USE_DEBUG) && !defined(PETSC_HAVE_SYCL)
602   if (monitor) Kokkos::single(Kokkos::PerTeam(team), [=]() { printf("%3d KSP Residual norm %14.12e \n", 0, (double)dp); });
603 #endif
604   if (dp < atol) {
605     metad->reason = KSP_CONVERGED_ATOL_NORMAL;
606     return PETSC_SUCCESS;
607   }
608   if (0 == maxit) {
609     metad->reason = KSP_DIVERGED_ITS;
610     return PETSC_SUCCESS;
611   }
612   i = 0;
613   do {
614     /*     beta <- r'z     */
615     parallel_reduce(
616       Kokkos::TeamVectorRange(team, Nblk), [=](const int idx, PetscScalar &dot) { dot += Zr[idx] * PetscConj(Rl[idx]); }, beta);
617     team.team_barrier();
618 #if PCBJKOKKOS_VERBOSE_LEVEL >= 6
619   #if defined(PETSC_USE_DEBUG) && !defined(PETSC_HAVE_SYCL)
620     Kokkos::single(Kokkos::PerTeam(team), [=]() { printf("%7d beta = Z.R = %22.14e \n", i, (double)beta); });
621   #endif
622 #endif
623     if (!i) {
624       if (beta == 0.0) {
625         metad->reason = KSP_DIVERGED_BREAKDOWN_BICG;
626         goto done;
627       }
628       /*     p <- z          */
629       parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) {
630         Pr[idx] = Zr[idx];
631         Pl[idx] = Zl[idx];
632       });
633     } else {
634       b = beta / betaold;
635       /*     p <- z + b* p   */
636       b2 = PetscConj(b);
637       parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) {
638         Pr[idx] = b * Pr[idx] + Zr[idx];
639         Pl[idx] = b2 * Pl[idx] + Zl[idx];
640       });
641     }
642     team.team_barrier();
643     betaold = beta;
644     /*     z <- Kp         */
645     static_cast<void>(MatMult(team, glb_Aai, glb_Aaj, glb_Aaa, r, ic, start, end, Pr, Zr));
646     static_cast<void>(MatMultTranspose(team, glb_Aai, glb_Aaj, glb_Aaa, r, ic, start, end, Pl, Zl));
647     /*     dpi <- z'p      */
648     parallel_reduce(
649       Kokkos::TeamVectorRange(team, Nblk), [=](const int idx, PetscScalar &lsum) { lsum += Zr[idx] * PetscConj(Pl[idx]); }, dpi);
650     team.team_barrier();
651     //
652     a   = beta / dpi; /*     a = beta/p'z    */
653     ma  = -a;
654     mac = PetscConj(ma);
655     /*     x <- x + ap     */
656     parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) {
657       XX[idx] = XX[idx] + a * Pr[idx];
658       Rr[idx] = Rr[idx] + ma * Zr[idx];
659       Rl[idx] = Rl[idx] + mac * Zl[idx];
660     });
661     team.team_barrier();
662     team.team_barrier();
663     /*    dp <- r'*r       */
664     parallel_reduce(
665       Kokkos::TeamVectorRange(team, Nblk), [=](const int idx, PetscScalar &lsum) { lsum += Rr[idx] * PetscConj(Rr[idx]); }, dpi);
666     team.team_barrier();
667     dp = PetscSqrtReal(PetscRealPart(dpi));
668 #if defined(PETSC_USE_DEBUG) && !defined(PETSC_HAVE_SYCL)
669     if (monitor) Kokkos::single(Kokkos::PerTeam(team), [=]() { printf("%3d KSP Residual norm %14.12e \n", i + 1, (double)dp); });
670 #endif
671     if (dp < atol) {
672       metad->reason = KSP_CONVERGED_ATOL_NORMAL;
673       goto done;
674     }
675     if (dp / r0 < rtol) {
676       metad->reason = KSP_CONVERGED_RTOL_NORMAL;
677       goto done;
678     }
679 #if defined(PETSC_USE_DEBUG) && !defined(PETSC_HAVE_SYCL)
680     if (dp / r0 > dtol) {
681       metad->reason = KSP_DIVERGED_DTOL;
682       Kokkos::single(Kokkos::PerTeam(team), [=]() { printf("ERROR block %d diverged: %d it, res=%e, r_0=%e\n", team.league_rank(), i, dp, r0); });
683       goto done;
684     }
685 #else
686     if (dp / r0 > dtol) {
687       metad->reason = KSP_DIVERGED_DTOL;
688       goto done;
689     }
690 #endif
691     if (i + 1 == maxit) {
692       metad->reason = KSP_DIVERGED_ITS;
693       goto done;
694     }
695     /* z <- Br  */
696     parallel_for(Kokkos::TeamVectorRange(team, Nblk), [=](int idx) {
697       Zr[idx] = Di[idx] * Rr[idx];
698       Zl[idx] = Di[idx] * Rl[idx];
699     });
700     i++;
701     team.team_barrier();
702   } while (i < maxit);
703 done:
704   // put x back into Plex order
705   parallel_for(Kokkos::TeamVectorRange(team, start, end), [=](int rowb) {
706     int rowa    = ic[rowb];
707     glb_x[rowa] = XX[rowb - start];
708   });
709   metad->its = i + 1;
710   if (1) {
711     int nnz;
712     parallel_reduce(
713       Kokkos::TeamVectorRange(team, start, end), [=](const int idx, int &lsum) { lsum += (glb_Aai[idx + 1] - glb_Aai[idx]); }, nnz);
714     metad->flops = 2 * (metad->its * (10 * Nblk + 2 * nnz) + 5 * Nblk);
715   } else {
716     metad->flops = 2 * (metad->its * (10 * Nblk + 2 * 50 * Nblk) + 5 * Nblk); // guess
717   }
718   return PETSC_SUCCESS;
719 }
720 
721 // KSP solver solve Ax = b; xout is output, bin is input
722 static PetscErrorCode PCApply_BJKOKKOS(PC pc, Vec bin, Vec xout)
723 {
724   PC_PCBJKOKKOS *jac = (PC_PCBJKOKKOS *)pc->data;
725   Mat            A = pc->pmat, Aseq = A;
726 
727   PetscFunctionBegin;
728   if (!A->spptr) {
729     Aseq = ((Mat_MPIAIJ *)A->data)->A; // MPI
730   }
731   PetscCall(MatSeqAIJKokkosSyncDevice(Aseq));
732   {
733     PetscInt           maxit = jac->ksp->max_it;
734     const PetscInt     conc = Kokkos::DefaultExecutionSpace().concurrency(), openmp = !!(conc < 1000), team_size = (openmp == 0 && PCBJKOKKOS_VEC_SIZE != 1) ? PCBJKOKKOS_TEAM_SIZE : 1;
735     const PetscInt     nwork = jac->nwork, nBlk = jac->nBlocks;
736     PetscScalar       *glb_xdata = NULL, *dummy;
737     PetscReal          rtol = jac->ksp->rtol, atol = jac->ksp->abstol, dtol = jac->ksp->divtol;
738     const PetscScalar *glb_idiag = jac->d_idiag_k->data(), *glb_bdata = NULL;
739     const PetscInt    *glb_Aai, *glb_Aaj, *d_bid_eqOffset = jac->d_bid_eqOffset_k->data();
740     const PetscScalar *glb_Aaa;
741     const PetscInt    *d_isicol = jac->d_isicol_k->data(), *d_isrow = jac->d_isrow_k->data();
742     PCFailedReason     pcreason;
743     KSPIndex           ksp_type_idx = jac->ksp_type_idx;
744     PetscMemType       mtype;
745     PetscContainer     container;
746     PetscInt           batch_sz;                // the number of repeated DMs, [DM_e_1, DM_e_2, DM_e_batch_sz, DM_i_1, ...]
747     VecScatter         plex_batch = NULL;       // not used
748     Vec                bvec;                    // a copy of b for scatter (just alias to bin now)
749     PetscBool          monitor  = jac->monitor; // captured
750     PetscInt           view_bid = jac->batch_target;
751     MatInfo            info;
752 
753     PetscCall(MatSeqAIJGetCSRAndMemType(Aseq, &glb_Aai, &glb_Aaj, &dummy, &mtype));
754     glb_Aaa       = dummy;
755     jac->max_nits = 0;
756     if (view_bid < 0) view_bid = 0;
757     PetscCall(MatGetInfo(A, MAT_LOCAL, &info));
758     // get field major is to map plex IO to/from block/field major
759     PetscCall(PetscObjectQuery((PetscObject)A, "plex_batch_is", (PetscObject *)&container));
760     if (container) {
761       PetscCall(VecDuplicate(bin, &bvec));
762       PetscCall(PetscContainerGetPointer(container, (void **)&plex_batch));
763       PetscCall(VecScatterBegin(plex_batch, bin, bvec, INSERT_VALUES, SCATTER_FORWARD));
764       PetscCall(VecScatterEnd(plex_batch, bin, bvec, INSERT_VALUES, SCATTER_FORWARD));
765       SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_USER, "No plex_batch_is -- require NO field major ordering for now");
766     } else {
767       bvec = bin;
768     }
769     // get x
770     PetscCall(VecGetArrayAndMemType(xout, &glb_xdata, &mtype));
771 #if defined(PETSC_HAVE_CUDA)
772     PetscCheck(PetscMemTypeDevice(mtype), PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "No GPU data for x %" PetscInt_FMT " != %" PetscInt_FMT, mtype, PETSC_MEMTYPE_DEVICE);
773 #endif
774     PetscCall(VecGetArrayReadAndMemType(bvec, &glb_bdata, &mtype));
775 #if defined(PETSC_HAVE_CUDA)
776     PetscCheck(PetscMemTypeDevice(mtype), PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "No GPU data for b");
777 #endif
778     // get batch size
779     PetscCall(PetscObjectQuery((PetscObject)A, "batch size", (PetscObject *)&container));
780     if (container) {
781       PetscInt *pNf = NULL;
782       PetscCall(PetscContainerGetPointer(container, (void **)&pNf));
783       batch_sz = *pNf; // number of times to repeat the DMs
784     } else batch_sz = 1;
785     PetscCheck(nBlk % batch_sz == 0, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "batch_sz = %" PetscInt_FMT ", nBlk = %" PetscInt_FMT, batch_sz, nBlk);
786     if (ksp_type_idx == BATCH_KSP_GMRES_IDX) { // KK solver - move PETSc data into Kokkos Views, setup solver, solve, move data out of Kokkos, process metadata (convergence tests, etc.)
787 #if defined(PETSC_HAVE_KOKKOS_KERNELS_GMRES)
788       int       Nsolves_team = jac->nsolves_team, fill_idx = 0;
789       int       Nloc    = jac->const_block_size; // same grids
790       const int Nsolves = nBlk;
791       const int nnz     = (int)info.nz_used / Nsolves;      // fix for variable grid size
792       if (Nsolves_team > batch_sz) Nsolves_team = batch_sz; // silently fix this
793       PetscCheck(jac->const_block_size, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "Kokkos (GMRES) solver requires constant block size (but can be made to work with species ordering or N_team==1)");
794       PetscCheck(Nsolves % Nsolves_team == 0, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "Nsolves.mod(Nsolves_team) != 0: Nsolves = %d, Nsolves_team = %d", Nsolves, Nsolves_team);
795       PetscCheck(((int)info.nz_used) % Nsolves == 0, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "info.nz_used.mod(Nsolves) != 0: info.nz_used = %g, Nsolves = %d", info.nz_used, Nsolves);
796   #if defined(PETSC_HAVE_CUDA)
797       nvtxRangePushA("gmres-kk");
798   #endif
799       Kokkos::View<PetscScalar **, layout, exec_space, Kokkos::MemoryTraits<Kokkos::Unmanaged>> inv_diag((PetscScalar *)glb_idiag, Nsolves, Nloc); // in correct order
800       if (!jac->rowOffsets) {
801         jac->rowOffsets   = new IntView("rowOffsets", Nsolves / Nsolves_team, Nloc + 1); // same grids
802         jac->colIndices   = new IntView("colIndices", Nsolves / Nsolves_team, nnz);
803         jac->batch_b      = new XYType("batch rhs", Nsolves, Nloc);
804         jac->batch_x      = new XYType("batch sol", Nsolves, Nloc);
805         jac->batch_values = new AMatrixValueView("batch values", Nsolves, nnz);
806         fill_idx          = 1;
807         PetscCall(PetscInfo(pc, "Setup indices Nloc=%d, nnz=%d\n", Nloc, nnz));
808       }
809       IntView          &rowOffsets   = *jac->rowOffsets;
810       IntView          &colIndices   = *jac->colIndices;
811       XYType           &batch_b      = *jac->batch_b;
812       XYType           &batch_x      = *jac->batch_x;
813       AMatrixValueView &batch_values = *jac->batch_values;
814 
815       Kokkos::deep_copy(batch_x, 0.);
816       PetscCall(PetscInfo(pc, "\tjac->n = %" PetscInt_FMT ", Nloc = %d, Nsolves = %d, nnz = %d, Nsolves_team = %d, league size = %d, maxit = %" PetscInt_FMT "\n", jac->n, Nloc, Nsolves, nnz, Nsolves_team, Nsolves / Nsolves_team, maxit));
817       Kokkos::parallel_for(
818         "rowOffsets+map", Kokkos::TeamPolicy<>(Nsolves, team_size, PCBJKOKKOS_VEC_SIZE), KOKKOS_LAMBDA(const team_member team) {
819           const int blkID = team.league_rank(), start = d_bid_eqOffset[blkID], end = d_bid_eqOffset[blkID + 1];
820           if (fill_idx) {
821             if (blkID % Nsolves_team == 0) {                                                        // first matrix on this member
822               Kokkos::parallel_for(Kokkos::TeamVectorRange(team, start, end), [=](const int rowb) { // Nloc
823                 int rowa                                           = d_isicol[rowb];
824                 int n                                              = glb_Aai[rowa + 1] - glb_Aai[rowa];
825                 rowOffsets(blkID / Nsolves_team, rowb + 1 - start) = n; // save sizes
826               });
827             }
828           }
829           // map b into field major space
830           Kokkos::parallel_for(Kokkos::TeamVectorRange(team, start, end), [=](int rowb) {
831             int rowa                     = d_isicol[rowb];
832             batch_b(blkID, rowb - start) = glb_bdata[rowa];
833           });
834         });
835       Kokkos::fence();
836       if (fill_idx) {
837         Kokkos::parallel_for(
838           "prefix sum", Kokkos::TeamPolicy<>(Nsolves / Nsolves_team, 1, 1), KOKKOS_LAMBDA(const team_member team) {
839             const int graphID      = team.league_rank();
840             rowOffsets(graphID, 0) = 0;
841             for (size_t i = 0; i < Nloc; ++i) rowOffsets(graphID, i + 1) += rowOffsets(graphID, i);
842           });
843         Kokkos::fence();
844       }
845       Kokkos::parallel_for(
846         "copy matrix", Kokkos::TeamPolicy<>(Nsolves /* /batch_sz */, team_size, PCBJKOKKOS_VEC_SIZE), KOKKOS_LAMBDA(const team_member team) {
847           const int blkID = team.league_rank(), start = d_bid_eqOffset[blkID], end = d_bid_eqOffset[blkID + 1], graphID = blkID / Nsolves_team;
848           Kokkos::parallel_for(Kokkos::TeamThreadRange(team, start, end), [=](const int rowb) {
849             int                rowa = d_isicol[rowb];
850             int                n    = glb_Aai[rowa + 1] - glb_Aai[rowa];
851             const PetscInt    *aj   = glb_Aaj + glb_Aai[rowa]; // global index
852             const PetscScalar *aa   = glb_Aaa + glb_Aai[rowa];
853             Kokkos::parallel_for(Kokkos::ThreadVectorRange(team, n), [=](const int &i) {
854               PetscScalar val = aa[i];
855               if (fill_idx && blkID % Nsolves_team == 0) colIndices(graphID, rowOffsets(graphID, rowb - start) + i) = d_isrow[aj[i]] - blkID * Nloc; // local" global - block start
856               batch_values(blkID, rowOffsets(graphID, rowb - start) + i) = val;
857             });
858           });
859         });
860       Kokkos::fence();
861       // setup solver
862       using ScalarType                = typename AMatrixValueView::non_const_value_type;
863       using MagnitudeType             = typename Kokkos::Details::ArithTraits<ScalarType>::mag_type;
864       using NormViewType              = Kokkos::View<MagnitudeType *, layout, exec_space>;
865       using Norm2DViewType            = Kokkos::View<MagnitudeType **, layout, exec_space>;
866       using Scalar3DViewType          = Kokkos::View<ScalarType ***, layout, exec_space>;
867       using IntViewType               = Kokkos::View<int *, layout, exec_space>;
868       using KrylovHandleType          = KokkosBatched::KrylovHandle<Norm2DViewType, IntViewType, Scalar3DViewType>;
869       const int        n_iterations   = maxit;
870       const int        team_size      = -1;
871       const int        vector_length  = -1;
872       const double     tol            = rtol;
873       const int        ortho_strategy = 0;
874       KrylovHandleType handle(Nsolves, Nsolves_team, n_iterations, true);
875       handle.Arnoldi_view = Scalar3DViewType("", Nsolves, n_iterations, Nloc + n_iterations + 3);
876       // solve
877       double time = Functor_TestBatchedTeamVectorGMRES<exec_space, AMatrixValueView, IntView, XYType, KrylovHandleType>(batch_values, inv_diag, rowOffsets, colIndices, batch_x, batch_b, Nsolves_team, team_size, vector_length, n_iterations, tol, ortho_strategy, 0, handle)
878                       .run(pc);
879       Kokkos::fence();
880       // get data back
881       Kokkos::parallel_for(
882         "map", Kokkos::TeamPolicy<>(Nsolves /* /batch_sz */, team_size, PCBJKOKKOS_VEC_SIZE), KOKKOS_LAMBDA(const team_member team) {
883           const int blkID = team.league_rank(), start = d_bid_eqOffset[blkID], end = d_bid_eqOffset[blkID + 1]; // 0
884           // map x into Plex/PETSc
885           Kokkos::parallel_for(Kokkos::TeamVectorRange(team, start, end), [=](int rowb) {
886             int rowa        = d_isicol[rowb];
887             glb_xdata[rowa] = batch_x(blkID, rowb - start);
888           });
889         });
890       // output assume species major - clone from Kokkos solvers
891   #if PCBJKOKKOS_VERBOSE_LEVEL >= 3
892     #if PCBJKOKKOS_VERBOSE_LEVEL >= 4
893       PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "Iterations\n"));
894     #else
895       PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "max iterations per species (gmres) :"));
896     #endif
897       for (PetscInt dmIdx = 0, s = 0, head = 0; dmIdx < jac->num_dms; dmIdx += batch_sz) {
898         for (PetscInt f = 0, idx = head; f < jac->dm_Nf[dmIdx]; f++, s++, idx++) {
899     #if PCBJKOKKOS_VERBOSE_LEVEL >= 4
900           PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "%2D:", s));
901           for (int bid = 0; bid < batch_sz; bid++) PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "%3D ", handle.get_iteration_host(idx + bid * jac->dm_Nf[dmIdx])));
902           PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "\n"));
903     #else
904           int count = 0, ii;
905           for (int bid = 0; bid < batch_sz; bid++) {
906             if ((ii = handle.get_iteration_host(idx + bid * jac->dm_Nf[dmIdx])) > count) count = ii;
907           }
908           PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "%3d", count));
909     #endif
910         }
911         head += batch_sz * jac->dm_Nf[dmIdx];
912       }
913     #if PCBJKOKKOS_VERBOSE_LEVEL == 3
914       PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "\n"));
915     #endif
916   #endif
917       // return error code, get max it
918       PetscInt count = 0, mbid = 0;
919       if (handle.is_converged_host()) {
920         pcreason = PC_NOERROR;
921         if (!jac->max_nits) {
922           for (int blkID = 0; blkID < nBlk; blkID++) {
923             if (handle.get_iteration_host(blkID) > jac->max_nits) {
924               jac->max_nits = handle.get_iteration_host(blkID);
925               mbid          = blkID;
926             }
927           }
928         }
929       } else {
930         PetscCall(PetscPrintf(PETSC_COMM_SELF, "There is at least one system that did not converge."));
931         pcreason = PC_SUBPC_ERROR;
932       }
933       // output - assume species major order
934       for (int blkID = 0; blkID < nBlk; blkID++) {
935         if (jac->reason) { // -pc_bjkokkos_ksp_converged_reason
936           if (jac->batch_target == blkID) {
937             if (batch_sz != 1)
938               PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "    Linear solve %s in %d iterations, batch %" PetscInt_FMT ", species %" PetscInt_FMT "\n", handle.is_converged_host(blkID) ? "converged" : "diverged", handle.get_iteration_host(blkID), blkID % batch_sz, blkID / batch_sz));
939             else PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "    Linear solve %s in %d iterations, block %" PetscInt_FMT "\n", handle.is_converged_host(blkID) ? "converged" : "diverged", handle.get_iteration_host(blkID), blkID));
940           } else if (jac->batch_target == -1 && handle.get_iteration_host(blkID) >= count) {
941             jac->max_nits = count = handle.get_iteration_host(blkID);
942             mbid                  = blkID;
943           }
944           if (!handle.is_converged_host(blkID)) PetscCall(PetscPrintf(PETSC_COMM_SELF, "ERROR species %d, batch %d did not converge with %d iterations\n", (int)(blkID / batch_sz), (int)blkID % batch_sz, handle.get_iteration_host(blkID)));
945         }
946       }
947       if (jac->batch_target == -1 && jac->reason) {
948         if (batch_sz != 1)
949           PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "    Linear solve %s in %d iteration, batch %" PetscInt_FMT ", specie %" PetscInt_FMT "\n", handle.is_converged_host(mbid) ? "converged" : "diverged", jac->max_nits, mbid % batch_sz, mbid / batch_sz));
950         else PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "    Linear solve %s in %d iteration, block %" PetscInt_FMT "\n", handle.is_converged_host(mbid) ? "converged" : "diverged", jac->max_nits, mbid));
951       }
952   #if defined(PETSC_HAVE_CUDA)
953       nvtxRangePop();
954   #endif
955 #else
956       SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_USER, "batch GMRES not supported");
957 #endif
958     } else { // Kokkos Krylov
959       using scr_mem_t    = Kokkos::DefaultExecutionSpace::scratch_memory_space;
960       using vect2D_scr_t = Kokkos::View<PetscScalar **, Kokkos::LayoutLeft, scr_mem_t>;
961       Kokkos::View<Batch_MetaData *, Kokkos::DefaultExecutionSpace> d_metadata("solver meta data", nBlk);
962       int                                                           stride_shared, stride_global, global_buff_words;
963       d_bid_eqOffset = jac->d_bid_eqOffset_k->data();
964       // solve each block independently
965       int scr_bytes_team_shared = 0, nShareVec = 0, nGlobBVec = 0;
966       if (jac->const_block_size) { // use shared memory for work vectors only if constant block size - todo: test efficiency loss
967         int         maximum_shared_mem_size = 64000;
968         PetscDevice device;
969         PetscCall(PetscDeviceGetDefault_Internal(&device));
970         PetscCall(PetscDeviceGetAttribute(device, PETSC_DEVICE_ATTR_SIZE_T_SHARED_MEM_PER_BLOCK, &maximum_shared_mem_size));
971         stride_shared = jac->const_block_size;                                                   // captured
972         nShareVec     = maximum_shared_mem_size / (jac->const_block_size * sizeof(PetscScalar)); // integer floor, number of vectors that fit in shared
973         if (nShareVec > nwork) nShareVec = nwork;
974         else nGlobBVec = nwork - nShareVec;
975         global_buff_words     = jac->n * nGlobBVec;
976         scr_bytes_team_shared = jac->const_block_size * nShareVec * sizeof(PetscScalar);
977       } else {
978         scr_bytes_team_shared = 0;
979         stride_shared         = 0;
980         global_buff_words     = jac->n * nwork;
981         nGlobBVec             = nwork; // not needed == fix
982       }
983       stride_global = jac->n; // captured
984 #if defined(PETSC_HAVE_CUDA)
985       nvtxRangePushA("batch-kokkos-solve");
986 #endif
987       Kokkos::View<PetscScalar *, Kokkos::DefaultExecutionSpace> d_work_vecs_k("workvectors", global_buff_words); // global work vectors
988       PetscCall(PetscInfo(pc, "\tn = %d. %d shared bytes/team, %d global mem bytes, rtol=%e, num blocks %d, team_size=%d, %d vector threads, %d shared vectors, %d global vectors\n", (int)jac->n, scr_bytes_team_shared, global_buff_words, rtol, (int)nBlk, (int)team_size, PCBJKOKKOS_VEC_SIZE, nShareVec, nGlobBVec));
989       PetscScalar *d_work_vecs = d_work_vecs_k.data();
990       Kokkos::parallel_for(
991         "Solve", Kokkos::TeamPolicy<Kokkos::LaunchBounds<256, 4>>(nBlk, team_size, PCBJKOKKOS_VEC_SIZE).set_scratch_size(PCBJKOKKOS_SHARED_LEVEL, Kokkos::PerTeam(scr_bytes_team_shared)), KOKKOS_LAMBDA(const team_member team) {
992           const int    blkID = team.league_rank(), start = d_bid_eqOffset[blkID], end = d_bid_eqOffset[blkID + 1];
993           vect2D_scr_t work_vecs_shared(team.team_scratch(PCBJKOKKOS_SHARED_LEVEL), end - start, nShareVec);
994           PetscScalar *work_buff_shared = work_vecs_shared.data();
995           PetscScalar *work_buff_global = &d_work_vecs[start]; // start inc'ed in
996           bool         print            = monitor && (blkID == view_bid);
997           switch (ksp_type_idx) {
998           case BATCH_KSP_BICG_IDX:
999             static_cast<void>(BJSolve_BICG(team, glb_Aai, glb_Aaj, glb_Aaa, d_isrow, d_isicol, work_buff_global, stride_global, nShareVec, work_buff_shared, stride_shared, rtol, atol, dtol, maxit, &d_metadata[blkID], start, end, glb_idiag, glb_bdata, glb_xdata, print));
1000             break;
1001           case BATCH_KSP_TFQMR_IDX:
1002             static_cast<void>(BJSolve_TFQMR(team, glb_Aai, glb_Aaj, glb_Aaa, d_isrow, d_isicol, work_buff_global, stride_global, nShareVec, work_buff_shared, stride_shared, rtol, atol, dtol, maxit, &d_metadata[blkID], start, end, glb_idiag, glb_bdata, glb_xdata, print));
1003             break;
1004           case BATCH_KSP_GMRES_IDX:
1005             //BJSolve_GMRES();
1006             break;
1007           default:
1008 #if defined(PETSC_USE_DEBUG) && !defined(PETSC_HAVE_SYCL)
1009             printf("Unknown KSP type %d\n", ksp_type_idx);
1010 #else
1011             /* void */;
1012 #endif
1013           }
1014         });
1015       Kokkos::fence();
1016 #if defined(PETSC_HAVE_CUDA)
1017       nvtxRangePop();
1018       nvtxRangePushA("Post-solve-metadata");
1019 #endif
1020       auto h_metadata = Kokkos::create_mirror(Kokkos::HostSpace::memory_space(), d_metadata);
1021       Kokkos::deep_copy(h_metadata, d_metadata);
1022       if (jac->reason) { // -pc_bjkokkos_ksp_converged_reason
1023 #if PCBJKOKKOS_VERBOSE_LEVEL >= 3
1024   #if PCBJKOKKOS_VERBOSE_LEVEL >= 4
1025         PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Iterations\n"));
1026   #endif
1027         // assume species major
1028   #if PCBJKOKKOS_VERBOSE_LEVEL < 4
1029         if (batch_sz != 1) PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "%s: max iterations per species:", ksp_type_idx == BATCH_KSP_BICG_IDX ? "bicg" : "tfqmr"));
1030         else PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "    Linear solve converged due to %s iterations ", ksp_type_idx == BATCH_KSP_BICG_IDX ? "bicg" : "tfqmr"));
1031   #endif
1032         for (PetscInt dmIdx = 0, s = 0, head = 0; dmIdx < jac->num_dms; dmIdx += batch_sz) {
1033           for (PetscInt f = 0, idx = head; f < jac->dm_Nf[dmIdx]; f++, s++, idx++) {
1034   #if PCBJKOKKOS_VERBOSE_LEVEL >= 4
1035             PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "%2" PetscInt_FMT ":", s));
1036             for (int bid = 0; bid < batch_sz; bid++) PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "%3" PetscInt_FMT " ", h_metadata[idx + bid * jac->dm_Nf[dmIdx]].its));
1037             PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "\n"));
1038   #else
1039             PetscInt count = 0;
1040             for (int bid = 0; bid < batch_sz; bid++) {
1041               if (h_metadata[idx + bid * jac->dm_Nf[dmIdx]].its > count) count = h_metadata[idx + bid * jac->dm_Nf[dmIdx]].its;
1042             }
1043             PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "%3" PetscInt_FMT " ", count));
1044   #endif
1045           }
1046           head += batch_sz * jac->dm_Nf[dmIdx];
1047         }
1048   #if PCBJKOKKOS_VERBOSE_LEVEL == 3
1049         PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "\n"));
1050   #endif
1051 #endif
1052         PetscInt count = 0, mbid = 0;
1053         for (int blkID = 0; blkID < nBlk; blkID++) {
1054           PetscCall(PetscLogGpuFlops((PetscLogDouble)h_metadata[blkID].flops));
1055 #if PCBJKOKKOS_VERBOSE_LEVEL < 3
1056           if (jac->batch_target == blkID) {
1057             if (batch_sz != 1)
1058               PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "    Linear solve converged due to %s iterations %d, batch %" PetscInt_FMT ", species %" PetscInt_FMT "\n", KSPConvergedReasons[h_metadata[blkID].reason], (int)h_metadata[blkID].its, blkID % batch_sz, blkID / batch_sz));
1059             else PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "    Linear solve converged due to %s iterations %d, block %d\n", KSPConvergedReasons[h_metadata[blkID].reason], (int)h_metadata[blkID].its, blkID));
1060           } else if (jac->batch_target == -1 && h_metadata[blkID].its >= count) {
1061             jac->max_nits = count = h_metadata[blkID].its;
1062             mbid                  = blkID;
1063           }
1064 #endif
1065 #if PCBJKOKKOS_VERBOSE_LEVEL > 0
1066           if (h_metadata[blkID].reason < 0) {
1067             PetscCall(PetscPrintf(PETSC_COMM_SELF, "ERROR reason=%s, its=%" PetscInt_FMT ". species %" PetscInt_FMT ", batch %" PetscInt_FMT "\n", KSPConvergedReasons[h_metadata[blkID].reason], h_metadata[blkID].its, blkID / batch_sz, blkID % batch_sz));
1068           }
1069 #endif
1070         }
1071         if (jac->batch_target == -1) {
1072           if (batch_sz != 1)
1073             PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "    Linear solve converged due to %s iterations %d, batch %" PetscInt_FMT ", species %" PetscInt_FMT "\n", KSPConvergedReasons[h_metadata[mbid].reason], (int)h_metadata[mbid].its, mbid % batch_sz, mbid / batch_sz));
1074           else PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "    Linear solve converged due to %s iterations %d, block %" PetscInt_FMT "\n", KSPConvergedReasons[h_metadata[mbid].reason], (int)h_metadata[mbid].its, mbid));
1075         }
1076       }
1077       for (int blkID = 0; blkID < nBlk; blkID++) {
1078         PetscCall(PetscLogGpuFlops((PetscLogDouble)h_metadata[blkID].flops));
1079 #if PCBJKOKKOS_VERBOSE_LEVEL > 0
1080         if (h_metadata[blkID].reason < 0) {
1081           PetscCall(PetscPrintf(PETSC_COMM_SELF, "ERROR reason=%s, its=%" PetscInt_FMT ". species %" PetscInt_FMT ", batch %" PetscInt_FMT "\n", KSPConvergedReasons[h_metadata[blkID].reason], h_metadata[blkID].its, blkID / batch_sz, blkID % batch_sz));
1082         }
1083 #endif
1084       }
1085       {
1086         int errsum;
1087         Kokkos::parallel_reduce(
1088           nBlk,
1089           KOKKOS_LAMBDA(const int idx, int &lsum) {
1090             if (d_metadata[idx].reason < 0) ++lsum;
1091           },
1092           errsum);
1093         pcreason = errsum ? PC_SUBPC_ERROR : PC_NOERROR;
1094         if (!errsum && !jac->max_nits) { // set max its to give back to top KSP
1095           for (int blkID = 0; blkID < nBlk; blkID++) {
1096             if (h_metadata[blkID].its > jac->max_nits) jac->max_nits = h_metadata[blkID].its;
1097           }
1098         } else if (errsum) {
1099           PetscCall(PetscPrintf(PETSC_COMM_SELF, "ERROR Kokkos batch solver did not converge in all solves\n"));
1100         }
1101       }
1102 #if defined(PETSC_HAVE_CUDA)
1103       nvtxRangePop();
1104 #endif
1105     } // end of Kokkos (not Kernels) solvers block
1106     PetscCall(VecRestoreArrayAndMemType(xout, &glb_xdata));
1107     PetscCall(VecRestoreArrayReadAndMemType(bvec, &glb_bdata));
1108     PetscCall(PCSetFailedReason(pc, pcreason));
1109     // map back to Plex space - not used
1110     if (plex_batch) {
1111       PetscCall(VecCopy(xout, bvec));
1112       PetscCall(VecScatterBegin(plex_batch, bvec, xout, INSERT_VALUES, SCATTER_REVERSE));
1113       PetscCall(VecScatterEnd(plex_batch, bvec, xout, INSERT_VALUES, SCATTER_REVERSE));
1114       PetscCall(VecDestroy(&bvec));
1115     }
1116   }
1117   PetscFunctionReturn(PETSC_SUCCESS);
1118 }
1119 
1120 static PetscErrorCode PCSetUp_BJKOKKOS(PC pc)
1121 {
1122   PC_PCBJKOKKOS *jac = (PC_PCBJKOKKOS *)pc->data;
1123   Mat            A = pc->pmat, Aseq = A; // use filtered block matrix, really "P"
1124   PetscBool      flg;
1125 
1126   PetscFunctionBegin;
1127   PetscCheck(!pc->useAmat, PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "No support for using 'use_amat'");
1128   PetscCheck(A, PetscObjectComm((PetscObject)A), PETSC_ERR_USER, "No matrix - A is used above");
1129   PetscCall(PetscObjectTypeCompareAny((PetscObject)A, &flg, MATSEQAIJKOKKOS, MATMPIAIJKOKKOS, MATAIJKOKKOS, ""));
1130   PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "must use '-[dm_]mat_type aijkokkos -[dm_]vec_type kokkos' for -pc_type bjkokkos");
1131   if (!A->spptr) {
1132     Aseq = ((Mat_MPIAIJ *)A->data)->A; // MPI
1133   }
1134   PetscCall(MatSeqAIJKokkosSyncDevice(Aseq));
1135   {
1136     PetscInt    Istart, Iend;
1137     PetscMPIInt rank;
1138     PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD, &rank));
1139     PetscCall(MatGetOwnershipRange(A, &Istart, &Iend));
1140     if (!jac->vec_diag) {
1141       Vec     *subX = NULL;
1142       DM       pack, *subDM = NULL;
1143       PetscInt nDMs, n, *block_sizes = NULL;
1144       IS       isrow, isicol;
1145       { // Permute the matrix to get a block diagonal system: d_isrow_k, d_isicol_k
1146         MatOrderingType rtype;
1147         const PetscInt *rowindices, *icolindices;
1148         rtype = MATORDERINGRCM;
1149         // get permutation. And invert. should we convert to local indices?
1150         PetscCall(MatGetOrdering(Aseq, rtype, &isrow, &isicol)); // only seems to work for seq matrix
1151         PetscCall(ISDestroy(&isrow));
1152         PetscCall(ISInvertPermutation(isicol, PETSC_DECIDE, &isrow)); // THIS IS BACKWARD -- isrow is inverse
1153         // if (rank==1) PetscCall(ISView(isicol, PETSC_VIEWER_STDOUT_SELF));
1154         if (1) {
1155           Mat mat_block_order; // debug
1156           PetscCall(ISShift(isicol, Istart, isicol));
1157           PetscCall(MatCreateSubMatrix(A, isicol, isicol, MAT_INITIAL_MATRIX, &mat_block_order));
1158           PetscCall(ISShift(isicol, -Istart, isicol));
1159           PetscCall(MatViewFromOptions(mat_block_order, NULL, "-ksp_batch_reorder_view"));
1160           PetscCall(MatDestroy(&mat_block_order));
1161         }
1162         PetscCall(ISGetIndices(isrow, &rowindices)); // local idx
1163         PetscCall(ISGetIndices(isicol, &icolindices));
1164         const Kokkos::View<PetscInt *, Kokkos::HostSpace, Kokkos::MemoryTraits<Kokkos::Unmanaged>> h_isrow_k((PetscInt *)rowindices, A->rmap->n);
1165         const Kokkos::View<PetscInt *, Kokkos::HostSpace, Kokkos::MemoryTraits<Kokkos::Unmanaged>> h_isicol_k((PetscInt *)icolindices, A->rmap->n);
1166         jac->d_isrow_k  = new Kokkos::View<PetscInt *>(Kokkos::create_mirror(DefaultMemorySpace(), h_isrow_k));
1167         jac->d_isicol_k = new Kokkos::View<PetscInt *>(Kokkos::create_mirror(DefaultMemorySpace(), h_isicol_k));
1168         Kokkos::deep_copy(*jac->d_isrow_k, h_isrow_k);
1169         Kokkos::deep_copy(*jac->d_isicol_k, h_isicol_k);
1170         PetscCall(ISRestoreIndices(isrow, &rowindices));
1171         PetscCall(ISRestoreIndices(isicol, &icolindices));
1172         // if (rank==1) PetscCall(ISView(isicol, PETSC_VIEWER_STDOUT_SELF));
1173       }
1174       // get block sizes & allocate vec_diag
1175       PetscCall(PCGetDM(pc, &pack));
1176       if (pack) {
1177         PetscCall(PetscObjectTypeCompare((PetscObject)pack, DMCOMPOSITE, &flg));
1178         if (flg) {
1179           PetscCall(DMCompositeGetNumberDM(pack, &nDMs));
1180           PetscCall(DMCreateGlobalVector(pack, &jac->vec_diag));
1181         } else pack = NULL; // flag for no DM
1182       }
1183       if (!jac->vec_diag) { // get 'nDMs' and sizes 'block_sizes' w/o DMComposite. User could provide ISs (todo)
1184         PetscInt        bsrt, bend, ncols, ntot = 0;
1185         const PetscInt *colsA, nloc = Iend - Istart;
1186         const PetscInt *rowindices, *icolindices;
1187         PetscCall(PetscMalloc1(nloc, &block_sizes)); // very inefficient, to big
1188         PetscCall(ISGetIndices(isrow, &rowindices));
1189         PetscCall(ISGetIndices(isicol, &icolindices));
1190         nDMs = 0;
1191         bsrt = 0;
1192         bend = 1;
1193         for (PetscInt row_B = 0; row_B < nloc; row_B++) { // for all rows in block diagonal space
1194           PetscInt rowA = icolindices[row_B], minj = PETSC_MAX_INT, maxj = 0;
1195           //PetscCall(PetscPrintf(PETSC_COMM_SELF, "\t[%d] rowA = %d\n",rank,rowA));
1196           PetscCall(MatGetRow(Aseq, rowA, &ncols, &colsA, NULL)); // not sorted in permutation
1197           PetscCheck(ncols, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "Empty row not supported: %" PetscInt_FMT "\n", row_B);
1198           for (PetscInt colj = 0; colj < ncols; colj++) {
1199             PetscInt colB = rowindices[colsA[colj]]; // use local idx
1200             //PetscCall(PetscPrintf(PETSC_COMM_SELF, "\t\t[%d] colB = %d\n",rank,colB));
1201             PetscCheck(colB >= 0 && colB < nloc, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "colB < 0: %" PetscInt_FMT "\n", colB);
1202             if (colB > maxj) maxj = colB;
1203             if (colB < minj) minj = colB;
1204           }
1205           PetscCall(MatRestoreRow(Aseq, rowA, &ncols, &colsA, NULL));
1206           if (minj >= bend) { // first column is > max of last block -- new block or last block
1207             //PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "\t\t finish block %d, N loc = %d (%d,%d)\n", nDMs+1, bend - bsrt,bsrt,bend));
1208             block_sizes[nDMs] = bend - bsrt;
1209             ntot += block_sizes[nDMs];
1210             PetscCheck(minj == bend, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "minj != bend: %" PetscInt_FMT " != %" PetscInt_FMT "\n", minj, bend);
1211             bsrt = bend;
1212             bend++; // start with size 1 in new block
1213             nDMs++;
1214           }
1215           if (maxj + 1 > bend) bend = maxj + 1;
1216           PetscCheck(minj >= bsrt || row_B == Iend - 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "%" PetscInt_FMT ") minj < bsrt: %" PetscInt_FMT " != %" PetscInt_FMT "\n", rowA, minj, bsrt);
1217           //PetscCall(PetscPrintf(PETSC_COMM_SELF, "[%d] %d) row %d.%d) cols %d : %d ; bsrt = %d, bend = %d\n",rank,row_B,nDMs,rowA,minj,maxj,bsrt,bend));
1218         }
1219         // do last block
1220         //PetscCall(PetscPrintf(PETSC_COMM_SELF, "\t\t\t [%d] finish block %d, N loc = %d (%d,%d)\n", rank, nDMs+1, bend - bsrt,bsrt,bend));
1221         block_sizes[nDMs] = bend - bsrt;
1222         ntot += block_sizes[nDMs];
1223         nDMs++;
1224         // cleanup
1225         PetscCheck(ntot == nloc, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "n total != n local: %" PetscInt_FMT " != %" PetscInt_FMT "\n", ntot, nloc);
1226         PetscCall(ISRestoreIndices(isrow, &rowindices));
1227         PetscCall(ISRestoreIndices(isicol, &icolindices));
1228         PetscCall(PetscRealloc(sizeof(PetscInt) * nDMs, &block_sizes));
1229         PetscCall(MatCreateVecs(A, &jac->vec_diag, NULL));
1230         PetscCall(PetscInfo(pc, "Setup Matrix based meta data (not DMComposite not attached to PC) %" PetscInt_FMT " sub domains\n", nDMs));
1231       }
1232       PetscCall(ISDestroy(&isrow));
1233       PetscCall(ISDestroy(&isicol));
1234       jac->num_dms = nDMs;
1235       PetscCall(VecGetLocalSize(jac->vec_diag, &n));
1236       jac->n         = n;
1237       jac->d_idiag_k = new Kokkos::View<PetscScalar *, Kokkos::LayoutRight>("idiag", n);
1238       // options
1239       PetscCall(PCBJKOKKOSCreateKSP_BJKOKKOS(pc));
1240       PetscCall(KSPSetFromOptions(jac->ksp));
1241       PetscCall(PetscObjectTypeCompareAny((PetscObject)jac->ksp, &flg, KSPBICG, ""));
1242       if (flg) {
1243         jac->ksp_type_idx = BATCH_KSP_BICG_IDX;
1244         jac->nwork        = 7;
1245       } else {
1246         PetscCall(PetscObjectTypeCompareAny((PetscObject)jac->ksp, &flg, KSPTFQMR, ""));
1247         if (flg) {
1248           jac->ksp_type_idx = BATCH_KSP_TFQMR_IDX;
1249           jac->nwork        = 10;
1250         } else {
1251           PetscCall(PetscObjectTypeCompareAny((PetscObject)jac->ksp, &flg, KSPGMRES, ""));
1252           PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Unsupported batch ksp type");
1253           jac->ksp_type_idx = BATCH_KSP_GMRES_IDX;
1254           jac->nwork        = 0;
1255         }
1256       }
1257       PetscOptionsBegin(PetscObjectComm((PetscObject)jac->ksp), ((PetscObject)jac->ksp)->prefix, "Options for Kokkos batch solver", "none");
1258       PetscCall(PetscOptionsBool("-ksp_converged_reason", "", "bjkokkos.kokkos.cxx.c", jac->reason, &jac->reason, NULL));
1259       PetscCall(PetscOptionsBool("-ksp_monitor", "", "bjkokkos.kokkos.cxx.c", jac->monitor, &jac->monitor, NULL));
1260       PetscCall(PetscOptionsInt("-ksp_batch_target", "", "bjkokkos.kokkos.cxx.c", jac->batch_target, &jac->batch_target, NULL));
1261       PetscCall(PetscOptionsInt("-ksp_batch_nsolves_team", "", "bjkokkos.kokkos.cxx.c", jac->nsolves_team, &jac->nsolves_team, NULL));
1262       PetscCheck(jac->batch_target < jac->num_dms, PETSC_COMM_WORLD, PETSC_ERR_ARG_WRONG, "-ksp_batch_target (%" PetscInt_FMT ") >= number of DMs (%" PetscInt_FMT ")", jac->batch_target, jac->num_dms);
1263       PetscOptionsEnd();
1264       // get blocks - jac->d_bid_eqOffset_k
1265       if (pack) {
1266         PetscCall(PetscMalloc(sizeof(*subX) * nDMs, &subX));
1267         PetscCall(PetscMalloc(sizeof(*subDM) * nDMs, &subDM));
1268       }
1269       PetscCall(PetscMalloc(sizeof(*jac->dm_Nf) * nDMs, &jac->dm_Nf));
1270       PetscCall(PetscInfo(pc, "Have %" PetscInt_FMT " blocks, n=%" PetscInt_FMT " rtol=%g type = %s\n", nDMs, n, (double)jac->ksp->rtol, ((PetscObject)jac->ksp)->type_name));
1271       if (pack) PetscCall(DMCompositeGetEntriesArray(pack, subDM));
1272       jac->nBlocks = 0;
1273       for (PetscInt ii = 0; ii < nDMs; ii++) {
1274         PetscInt Nf;
1275         if (subDM) {
1276           DM           dm = subDM[ii];
1277           PetscSection section;
1278           PetscCall(DMGetLocalSection(dm, &section));
1279           PetscCall(PetscSectionGetNumFields(section, &Nf));
1280         } else Nf = 1;
1281         jac->nBlocks += Nf;
1282 #if PCBJKOKKOS_VERBOSE_LEVEL <= 2
1283         if (ii == 0) PetscCall(PetscInfo(pc, "%" PetscInt_FMT ") %" PetscInt_FMT " blocks (%" PetscInt_FMT " total)\n", ii, Nf, jac->nBlocks));
1284 #else
1285         PetscCall(PetscInfo(pc, "%" PetscInt_FMT ") %" PetscInt_FMT " blocks (%" PetscInt_FMT " total)\n", ii, Nf, jac->nBlocks));
1286 #endif
1287         jac->dm_Nf[ii] = Nf;
1288       }
1289       { // d_bid_eqOffset_k
1290         Kokkos::View<PetscInt *, Kokkos::LayoutRight, Kokkos::HostSpace> h_block_offsets("block_offsets", jac->nBlocks + 1);
1291         if (pack) PetscCall(DMCompositeGetAccessArray(pack, jac->vec_diag, nDMs, NULL, subX));
1292         h_block_offsets[0]    = 0;
1293         jac->const_block_size = -1;
1294         for (PetscInt ii = 0, idx = 0; ii < nDMs; ii++) {
1295           PetscInt nloc, nblk;
1296           if (pack) PetscCall(VecGetSize(subX[ii], &nloc));
1297           else nloc = block_sizes[ii];
1298           nblk = nloc / jac->dm_Nf[ii];
1299           PetscCheck(nloc % jac->dm_Nf[ii] == 0, PetscObjectComm((PetscObject)pc), PETSC_ERR_USER, "nloc%%jac->dm_Nf[ii] (%" PetscInt_FMT ") != 0 DMs", nloc % jac->dm_Nf[ii]);
1300           for (PetscInt jj = 0; jj < jac->dm_Nf[ii]; jj++, idx++) {
1301             h_block_offsets[idx + 1] = h_block_offsets[idx] + nblk;
1302 #if PCBJKOKKOS_VERBOSE_LEVEL <= 2
1303             if (idx == 0) PetscCall(PetscInfo(pc, "\t%" PetscInt_FMT ") Add block with %" PetscInt_FMT " equations of %" PetscInt_FMT "\n", idx + 1, nblk, jac->nBlocks));
1304 #else
1305             PetscCall(PetscInfo(pc, "\t%" PetscInt_FMT ") Add block with %" PetscInt_FMT " equations of %" PetscInt_FMT "\n", idx + 1, nblk, jac->nBlocks));
1306 #endif
1307             if (jac->const_block_size == -1) jac->const_block_size = nblk;
1308             else if (jac->const_block_size > 0 && jac->const_block_size != nblk) jac->const_block_size = 0;
1309           }
1310         }
1311         if (pack) {
1312           PetscCall(DMCompositeRestoreAccessArray(pack, jac->vec_diag, jac->nBlocks, NULL, subX));
1313           PetscCall(PetscFree(subX));
1314           PetscCall(PetscFree(subDM));
1315         }
1316         jac->d_bid_eqOffset_k = new Kokkos::View<PetscInt *, Kokkos::LayoutRight>(Kokkos::create_mirror(Kokkos::DefaultExecutionSpace::memory_space(), h_block_offsets));
1317         Kokkos::deep_copy(*jac->d_bid_eqOffset_k, h_block_offsets);
1318       }
1319       if (!pack) PetscCall(PetscFree(block_sizes));
1320     }
1321     { // get jac->d_idiag_k (PC setup),
1322       const PetscInt    *d_ai, *d_aj;
1323       const PetscScalar *d_aa;
1324       const PetscInt     conc = Kokkos::DefaultExecutionSpace().concurrency(), openmp = !!(conc < 1000), team_size = (openmp == 0 && PCBJKOKKOS_VEC_SIZE != 1) ? PCBJKOKKOS_TEAM_SIZE : 1;
1325       const PetscInt    *d_bid_eqOffset = jac->d_bid_eqOffset_k->data(), *r = jac->d_isrow_k->data(), *ic = jac->d_isicol_k->data();
1326       PetscScalar       *d_idiag = jac->d_idiag_k->data(), *dummy;
1327       PetscMemType       mtype;
1328       PetscCall(MatSeqAIJGetCSRAndMemType(Aseq, &d_ai, &d_aj, &dummy, &mtype));
1329       d_aa = dummy;
1330       Kokkos::parallel_for(
1331         "Diag", Kokkos::TeamPolicy<>(jac->nBlocks, team_size, PCBJKOKKOS_VEC_SIZE), KOKKOS_LAMBDA(const team_member team) {
1332           const PetscInt blkID = team.league_rank();
1333           Kokkos::parallel_for(Kokkos::TeamThreadRange(team, d_bid_eqOffset[blkID], d_bid_eqOffset[blkID + 1]), [=](const int rowb) {
1334             const PetscInt     rowa = ic[rowb], ai = d_ai[rowa], *aj = d_aj + ai; // grab original data
1335             const PetscScalar *aa   = d_aa + ai;
1336             const PetscInt     nrow = d_ai[rowa + 1] - ai;
1337             int                found;
1338             Kokkos::parallel_reduce(
1339               Kokkos::ThreadVectorRange(team, nrow),
1340               [=](const int &j, int &count) {
1341                 const PetscInt colb = r[aj[j]];
1342                 if (colb == rowb) {
1343                   d_idiag[rowb] = 1. / aa[j];
1344                   count++;
1345                 }
1346               },
1347               found);
1348 #if defined(PETSC_USE_DEBUG) && !defined(PETSC_HAVE_SYCL)
1349             if (found != 1) Kokkos::single(Kokkos::PerThread(team), [=]() { printf("ERRORrow %d) found = %d\n", rowb, found); });
1350 #endif
1351           });
1352         });
1353     }
1354   }
1355   PetscFunctionReturn(PETSC_SUCCESS);
1356 }
1357 
1358 /* Default destroy, if it has never been setup */
1359 static PetscErrorCode PCReset_BJKOKKOS(PC pc)
1360 {
1361   PC_PCBJKOKKOS *jac = (PC_PCBJKOKKOS *)pc->data;
1362 
1363   PetscFunctionBegin;
1364   PetscCall(KSPDestroy(&jac->ksp));
1365   PetscCall(VecDestroy(&jac->vec_diag));
1366   if (jac->d_bid_eqOffset_k) delete jac->d_bid_eqOffset_k;
1367   if (jac->d_idiag_k) delete jac->d_idiag_k;
1368   if (jac->d_isrow_k) delete jac->d_isrow_k;
1369   if (jac->d_isicol_k) delete jac->d_isicol_k;
1370   jac->d_bid_eqOffset_k = NULL;
1371   jac->d_idiag_k        = NULL;
1372   jac->d_isrow_k        = NULL;
1373   jac->d_isicol_k       = NULL;
1374   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCBJKOKKOSGetKSP_C", NULL)); // not published now (causes configure errors)
1375   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCBJKOKKOSSetKSP_C", NULL));
1376   PetscCall(PetscFree(jac->dm_Nf));
1377   jac->dm_Nf = NULL;
1378   if (jac->rowOffsets) delete jac->rowOffsets;
1379   if (jac->colIndices) delete jac->colIndices;
1380   if (jac->batch_b) delete jac->batch_b;
1381   if (jac->batch_x) delete jac->batch_x;
1382   if (jac->batch_values) delete jac->batch_values;
1383   jac->rowOffsets   = NULL;
1384   jac->colIndices   = NULL;
1385   jac->batch_b      = NULL;
1386   jac->batch_x      = NULL;
1387   jac->batch_values = NULL;
1388 
1389   PetscFunctionReturn(PETSC_SUCCESS);
1390 }
1391 
1392 static PetscErrorCode PCDestroy_BJKOKKOS(PC pc)
1393 {
1394   PetscFunctionBegin;
1395   PetscCall(PCReset_BJKOKKOS(pc));
1396   PetscCall(PetscFree(pc->data));
1397   PetscFunctionReturn(PETSC_SUCCESS);
1398 }
1399 
1400 static PetscErrorCode PCView_BJKOKKOS(PC pc, PetscViewer viewer)
1401 {
1402   PC_PCBJKOKKOS *jac = (PC_PCBJKOKKOS *)pc->data;
1403   PetscBool      iascii;
1404 
1405   PetscFunctionBegin;
1406   if (!jac->ksp) PetscCall(PCBJKOKKOSCreateKSP_BJKOKKOS(pc));
1407   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
1408   if (iascii) {
1409     PetscCall(PetscViewerASCIIPrintf(viewer, "  Batched device linear solver: Krylov (KSP) method with Jacobi preconditioning\n"));
1410     PetscCall(PetscViewerASCIIPrintf(viewer, "\t\tnwork = %" PetscInt_FMT ", rel tol = %e, abs tol = %e, div tol = %e, max it =%" PetscInt_FMT ", type = %s\n", jac->nwork, jac->ksp->rtol, jac->ksp->abstol, jac->ksp->divtol, jac->ksp->max_it,
1411                                      ((PetscObject)jac->ksp)->type_name));
1412   }
1413   PetscFunctionReturn(PETSC_SUCCESS);
1414 }
1415 
1416 static PetscErrorCode PCSetFromOptions_BJKOKKOS(PC pc, PetscOptionItems *PetscOptionsObject)
1417 {
1418   PetscFunctionBegin;
1419   PetscOptionsHeadBegin(PetscOptionsObject, "PC BJKOKKOS options");
1420   PetscOptionsHeadEnd();
1421   PetscFunctionReturn(PETSC_SUCCESS);
1422 }
1423 
1424 static PetscErrorCode PCBJKOKKOSSetKSP_BJKOKKOS(PC pc, KSP ksp)
1425 {
1426   PC_PCBJKOKKOS *jac = (PC_PCBJKOKKOS *)pc->data;
1427 
1428   PetscFunctionBegin;
1429   PetscCall(PetscObjectReference((PetscObject)ksp));
1430   PetscCall(KSPDestroy(&jac->ksp));
1431   jac->ksp = ksp;
1432   PetscFunctionReturn(PETSC_SUCCESS);
1433 }
1434 
1435 /*@C
1436    PCBJKOKKOSSetKSP - Sets the `KSP` context for `PCBJKOKKOS`
1437 
1438    Collective
1439 
1440    Input Parameters:
1441 +  pc - the `PCBJKOKKOS` preconditioner context
1442 -  ksp - the `KSP` solver
1443 
1444    Level: advanced
1445 
1446    Notes:
1447    The `PC` and the `KSP` must have the same communicator
1448 
1449    If the `PC` is not `PCBJKOKKOS` this function returns without doing anything
1450 
1451 ,seealso: `PCBJKOKKOSGetKSP()`, `PCBJKOKKOS`
1452 @*/
1453 PetscErrorCode PCBJKOKKOSSetKSP(PC pc, KSP ksp)
1454 {
1455   PetscFunctionBegin;
1456   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
1457   PetscValidHeaderSpecific(ksp, KSP_CLASSID, 2);
1458   PetscCheckSameComm(pc, 1, ksp, 2);
1459   PetscTryMethod(pc, "PCBJKOKKOSSetKSP_C", (PC, KSP), (pc, ksp));
1460   PetscFunctionReturn(PETSC_SUCCESS);
1461 }
1462 
1463 static PetscErrorCode PCBJKOKKOSGetKSP_BJKOKKOS(PC pc, KSP *ksp)
1464 {
1465   PC_PCBJKOKKOS *jac = (PC_PCBJKOKKOS *)pc->data;
1466 
1467   PetscFunctionBegin;
1468   if (!jac->ksp) PetscCall(PCBJKOKKOSCreateKSP_BJKOKKOS(pc));
1469   *ksp = jac->ksp;
1470   PetscFunctionReturn(PETSC_SUCCESS);
1471 }
1472 
1473 /*@C
1474    PCBJKOKKOSGetKSP - Gets the `KSP` context for the `PCBJKOKKOS` preconditioner
1475 
1476    Not Collective but `KSP` returned is parallel if `PC` was parallel
1477 
1478    Input Parameter:
1479 .  pc - the preconditioner context
1480 
1481    Output Parameter:
1482 .  ksp - the `KSP` solver
1483 
1484    Level: advanced
1485 
1486    Notes:
1487    You must call `KSPSetUp()` before calling `PCBJKOKKOSGetKSP()`.
1488 
1489    If the `PC` is not a `PCBJKOKKOS` object it raises an error
1490 
1491 .seealso: `PCBJKOKKOS`, `PCBJKOKKOSSetKSP()`
1492 @*/
1493 PetscErrorCode PCBJKOKKOSGetKSP(PC pc, KSP *ksp)
1494 {
1495   PetscFunctionBegin;
1496   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
1497   PetscValidPointer(ksp, 2);
1498   PetscUseMethod(pc, "PCBJKOKKOSGetKSP_C", (PC, KSP *), (pc, ksp));
1499   PetscFunctionReturn(PETSC_SUCCESS);
1500 }
1501 
1502 /*MC
1503      PCBJKOKKOS -  Defines a preconditioner that applies a Krylov solver and preconditioner to the blocks in a `MATSEQAIJ` matrix on the GPU using Kokkos
1504 
1505    Options Database Key:
1506 .     -pc_bjkokkos_ - options prefix for its `KSP` options
1507 
1508    Level: intermediate
1509 
1510    Note:
1511     For use with -ksp_type preonly to bypass any computation on the CPU
1512 
1513    Developer Notes:
1514    The documentation is incomplete. Is this a block Jacobi preconditioner?
1515 
1516    Why does it have its own `KSP`? Where is the `KSP` run if used with -ksp_type preonly?
1517 
1518 .seealso: `PCCreate()`, `PCSetType()`, `PCType`, `PC`, `PCBJACOBI`,
1519           `PCSHELL`, `PCCOMPOSITE`, `PCSetUseAmat()`, `PCBJKOKKOSGetKSP()`
1520 M*/
1521 
1522 PETSC_EXTERN PetscErrorCode PCCreate_BJKOKKOS(PC pc)
1523 {
1524   PC_PCBJKOKKOS *jac;
1525 
1526   PetscFunctionBegin;
1527   PetscCall(PetscNew(&jac));
1528   pc->data = (void *)jac;
1529 
1530   jac->ksp              = NULL;
1531   jac->vec_diag         = NULL;
1532   jac->d_bid_eqOffset_k = NULL;
1533   jac->d_idiag_k        = NULL;
1534   jac->d_isrow_k        = NULL;
1535   jac->d_isicol_k       = NULL;
1536   jac->nBlocks          = 1;
1537   jac->max_nits         = 0;
1538 
1539   PetscCall(PetscMemzero(pc->ops, sizeof(struct _PCOps)));
1540   pc->ops->apply          = PCApply_BJKOKKOS;
1541   pc->ops->applytranspose = NULL;
1542   pc->ops->setup          = PCSetUp_BJKOKKOS;
1543   pc->ops->reset          = PCReset_BJKOKKOS;
1544   pc->ops->destroy        = PCDestroy_BJKOKKOS;
1545   pc->ops->setfromoptions = PCSetFromOptions_BJKOKKOS;
1546   pc->ops->view           = PCView_BJKOKKOS;
1547 
1548   jac->rowOffsets   = NULL;
1549   jac->colIndices   = NULL;
1550   jac->batch_b      = NULL;
1551   jac->batch_x      = NULL;
1552   jac->batch_values = NULL;
1553 
1554   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCBJKOKKOSGetKSP_C", PCBJKOKKOSGetKSP_BJKOKKOS));
1555   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCBJKOKKOSSetKSP_C", PCBJKOKKOSSetKSP_BJKOKKOS));
1556   PetscFunctionReturn(PETSC_SUCCESS);
1557 }
1558